{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f619633e",
   "metadata": {},
   "source": [
    "# 频谱泄露"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1ffdd6bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#导入使用的库\n",
    "import numpy as np\n",
    "import pylab as pl\n",
    "\n",
    "fs = 8000\n",
    "N = 512\n",
    "t = np.arange(0, 1, 1/fs)\n",
    "x = np.sin(2*np.pi*100*t)+2*np.sin(2*np.pi*400*t)\n",
    "\n",
    "xs = x[:N]\n",
    "xf = np.fft.rfft(xs)/N\n",
    "freqs = np.linspace(0, int(fs/2), int(N/2+1))\n",
    "xfp = np.abs(xf)\n",
    "pl.figure()\n",
    "pl.subplot(211)\n",
    "pl.plot(t[:N], xs)\n",
    "pl.xlabel(u\"Time(S)\")\n",
    "pl.subplot(212)\n",
    "pl.plot(freqs, xfp)\n",
    "pl.xlabel(u\"Freq(Hz)\")\n",
    "pl.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b922a8bf",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
